What is the difference between BHQ-1 and BHQ-2 in terms of applications when we use dual labelled DNA probes

The difference is the effective quenching range of the two BHQs. BHQ1 is used to quench green and yellow dyes, such as FAM, TET, or HEX. BHQ2 is better for orange or red dyes, such as TAMRA, Texas Red, or Cy 5. You can use a BHQ1 quenched oligo with a BHQ2 quenched oligo together in a multiplex reaction.